We know Bloch state has a phase undetermined, so $\Psi_k \to \Psi_k' = e^{i\theta(k)}\Psi_k$ is still the same eigenstate.
My question: Are there some restriction on $\theta(k)$ except to be a real ...

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...

In the derivations of the Aharonov-Bohm phase, it is directly mentioned that due to the introduction of the vector potential $A$, an extra phase is introduced into the wavefunction for case $A\neq0$ ...

Suppose we have normalized states $| n(\vec{R})\rangle$ indexed by continuous variable $\vec{R}$. Then fixing our choice of gauge and ignoring dynamic phase, the phase difference between two states ...

The question is not so much about the theorem, but more about what it means in this context: see this link.
So yes, because of Bloch's theorem the Hamiltonian eigenstates in a crystalline system can ...

The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in ...

I had read some papers that have mentioned the geometric phase (Berry phase) can be used to detect the quantum phase transitions in a quantum many-body system. My question is: How is it measured in ...

I have been reading about the quantum hall effect during which i had to read about the AB effect used in the Laughlin gauge argument. In many sources, it is directly assumed that the flux quantum in ...

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...

I have a question essentially the same with this one "Aharonov-Bohm Effect and Flux Quantization in superconductors" which is why we can say the flux is quantized in superconducting disk but not in AB ...

The so-called artificial gauge fields are actually the Berry connection. They could be $U(1)$ or $SU(N)$ which depends on the level degeneracy.
For simplicity, let's focus on $U(1)$ artificial gauge ...

Consider a hamiltonian with degeneracies of energy in parameter space $(R)$.Now the Geometric phase(Wilczek Zee Potential) will acquire a non abelian nature.
To prove the non abelian nature of Wilczek ...

Quantum phase arises when a spin-j state is sent through a sequence of transitions that return it to its original position. For example with spin-1/2, a state picks up a complex phase of $\pi/4$ when ...